Playing an opening 2-1

I have learned from Stick's rollouts and from ExtremeGammon and various coaches that it is generally right to play 2-1 by moving a checker from my 13 point to 11 point and then slotting my 5 point (6-5).

But the other day, I noticed that when I was trailing 2away/1away POST CRAWFORD ExtremeGammon said it was wrong to slot, but better to split the 1 by playing 24/23.  I then checked to see how ExtremeGammon plays it at DMP (1away/1away), and at that score it slots!

I could not understand the reason for the difference, so I asked one of my good friend and mentors, David Rockwell, to explain this to me, and here is his response:

From David:

This is correct.  2a will be doubling after 2 rolls, one for each player.  1a will drop whenever 2a is winning.  2a doesn't get to play the positions where he stands well.  He has to start over.  Slotting doesn't work because it creates situations when you stand very well (the shot is missed) and situations where you stand very poorly (the shot is hit).  You end up playing only the positions where the shot is hit.


Here's a numerical example.  Imagine there are only 4 equities instead of 1296. 


Sequence 1 equity:


0.2, 0.1, -.05, -.15 / Average equity of .025


At this score, your positive equity is reset to zero since 1a drops and you have to start the game over.  So the sequence becomes:


0.0, 0.0, -.05, -.15 / Average equity of -.050


Sequence 2 equity:


0.02, -.02, -.04, -.06 / Average equity of -.025


At score equity:


0.0, -.02, -.04, -.06 / Average equity of -.030


So, at DMP, you play sequence 1.  ATS (at score 2a1a) you play sequence 2.  You want to make a play at 2a1a which is never or seldom very bad.  Ideally, the equities are bunched just barely under 0.0. 


I did GNU rollouts a couple of years ago at this score.  I never went past 5k, so they are not necessarily going to be the final word.  Slotting is generally a weak play.  This was already known.  Woolsey has written about it.  What wasn't known is that Up plays such as 41 (24-20, 24-23) are strong at this score.  Playing Up with 41 and 51 (24-18 actually Nactated as R, Run) was best and it was close with 21, 32 & 43.  Playing Up will seldom give you an advantage.  But, it won't give you a big disadvantage either unless the responder points on head.  That's exactly what you want at this score.


Reminder of the obvious - This is only true when the 2a player wins the opening roll.  When 1a wins the opening roll, he just makes the DMP play.  He will take almost everything, so he gets to play his strong positions.